Is this normal threenager behaviour?

I'll preface it with he can be the sweetest boy. He is well behaved at daycare. At playgrounds he is kind and considerate and will wait his turn.

With us however...

He is extremely moody. Prone to somewhat violent tantrums (sometimes multiple times per day). He can be defiant and shout "NO!!!" in our faces to calm demands for eating dinner or not throwing his toys, or, most importantly, to not hurt his 6 month sister.

Bringing his sister home was tough for the first two weeks, then things gradually got better. But now I feel this past month(s?) he has been increasingly volatile. My gut tells me it's partly jealousy related because of the baby. I'm breastfeeding, so I can't be away from her for too long. She's also quite early on a few milestones (already crawling), so she's not happy to sit in the pram or carrier for too long. I feel stretched very thin.

My partner does his best, but he suffers from chronic fatigue and gets overwhelmed easily. Neither of us are sleeping well. Both kids are prone to 5am wake ups (I'm currently up multiple times a night settling the baby too). We live in a small house so things feel claustrophobic within 30 mins of waking up.

Examples of my toddlers behaviour on a bad day: sulking, whining, snatching toys off sister, demanding we do everything for him, doesn't respond to discipline (any kind, but we are trying our best to be patient and firm), hitting/pinching sister, then incessantly following us around when we remove her from his reach. For example I will close the bedroom door and lock it (dad is in living room with toddler) so he can't hurt her. Calmy telling him it's not ok and we will come back out when he's ready to be kind and gentle. Toddler proceeds to kick and hit door and scream to let him in. If partner pryes him away from door he will assault him. 3 year olds are surprisingly strong. We cannot put him anywhere he won't hurt himself or his surroundings so sometimes we have to physically restrain him or put him outside where he will proceed to have a full meltdown and we just have to wait it out. I feel so bad for the neighbours.

Episodes like that happen out of the blue. Ie we'll be on the playmat just hanging out and then all of a sudden he will start being rough with his sister. Although I can always tell that a bad mood is simmering beneath the surface.

He is too young to explain why he is frustrated etc.

We have taken to going on outings very early to get us all out of the house to prevent starting every day like this. But man is it hard. I just need a good night's sleep.

Is this norma behaviour? It's so heartbreaking seeing your little man struggle so much.